1. Today’s agenda: Electric Current. You must know the definition of current, and be able to use it in solving problems. Current Density. You must understand the difference between current and current density, and be able to use current density in solving problems. Ohm’s Law and Resistance. You must be able to use Ohm’s Law and electrical resistance in solving circuit problems. Resistivity. You must understand the relationship between resistance and resistivity, and be able to use calculate resistivity and associated quantities. Temperature Dependence of Resistivity. You must be able to use the temperature coefficient of resistivity to solve problems involving changing temperatures.

2. Temperature Dependence of Resistivity Many materials have resistivities that depend on temperature. We can model* this temperature dependence by an equation of the form where  0 is the resistivity at temperature T 0, and  is the temperature coefficient of resistivity. *T 0 is a reference temperature, often taken to be 0 °C or 20 °C. This approximation can be used if the temperature range is “not too great;” i.e. 100 °C or so.

3. Resistance thermometers made of carbon (inexpensive) and platinum (expensive) are widely used to measure very low temperatures.

4. Example: a carbon resistance thermometer in the shape of a cylinder 1 cm long and 4 mm in diameter is attached to a sample. The thermometer has a resistance of 0.030 . What is the temperature of the sample? This is the starting equation: We use the thermometer dimensions to calculate the resistivity when the resistance is 0.03 , and use the above equation directly. We can look up the resistivity of carbon at 20  C. Or we can rewrite the equation in terms or R. Let’s first do the calculation using resistivity.

5. Example: a carbon resistance thermometer in the shape of a cylinder 1 cm long and 4 mm in diameter is attached to a sample. The thermometer has a resistance of 0.030 . What is the temperature of the sample? The resistivity of carbon at 20  C is

6. Example: a carbon resistance thermometer in the shape of a cylinder 1 cm long and 4 mm in diameter is attached to a sample. The thermometer has a resistance of 0.030 . What is the temperature of the sample?

7. Alternatively, we can use the resistivity of carbon at 20  C to calculate the resistance at 20  C. This is the resistance at 20  C.

8. Example: a carbon resistance thermometer in the shape of a cylinder 1 cm long and 4 mm in diameter is attached to a sample. The thermometer has a resistance of 0.030 . What is the temperature of the sample? If we assume A/L = A 0 /L 0, then

9. Example: a carbon resistance thermometer in the shape of a cylinder 1 cm long and 4 mm in diameter is attached to a sample. The thermometer has a resistance of 0.030 . What is the temperature of the sample? The result is very sensitive to significant figures in resistivity and .